You may wish to try this, as it fixed an X-box issue,
http://forums.verizon.com/t5/FiOS-Internet/Cannot-connect-to-xbox-live/m-p/696360#U696360
The PS3 should allow you to put in a fixed address and then uses your router as DNS. or 4.4.4.4 as mentioned in the X-box post.
Also you may need to check the plug and play settings in the router as it may not allow the router to open ports for port forwarding.
See port forwarding here. I say it may be better to lock in the IP to a fixed address on your network, and check the port forwarding, rather that enable plug and play on the router if it is off. Though plug and play, makes things easier, it may also open up some security issues.
Verizon is fairly security consious, and usually airs on the secure side, as where I have seen some scarry things with some cable companies in regards to security.